Critical Dynamics of Spin Boson Model

TL;DR

This paper investigates the critical dynamics of the spin-boson model near quantum phase transitions using a universal Schwinger--Keldysh approach, revealing the critical exponents and temperature dependence of the coupling.

Contribution

It introduces a universal theoretical framework for analyzing the spin-boson model's critical behavior applicable for spectral exponents s ≤ 1.

Findings

Quantum phase transition observed for s=1 and s≈1

Critical magnetization exponent matches hyperscaling predictions

Critical coupling depends on temperature in the ohmic case

Abstract

In this work, we study the low-energy properties of the spin-boson model (SBM), which describes the dynamics of a 1/2 spin associated with a thermostat characterized by a power law spectral density, $f(\omega)\propto \omega^s$. The theoretical description is constructed in the Schwinger--Keldysh technique, based on the representation of the 1/2-spin by Majorana spinors. We study the critical dynamics of the system near the quantum phase transition by constructing and analyzing the system of renormalization group equations. Our theoretical approach is more universal, contrary to the one based on quantum-classical mapping, since it is applicable for $s\leq 1$. We show that in both the ohmic case $s=1$, and the weakly subohmic case $s\lesssim 1$, the second order quantum phase transition is observed in the model considered, and the critical magnetization exponent agrees with the exact hyperscaling result, $1/\delta=(1-s)/(1+s)$. Furthermore, we obtain the dependence of the critical value of the spin-boson coupling constant on the temperature of the ohmic bosonic thermal bath.